I would not recommend a Christian woman “pursue” a Christian man. However, I also believe she can do more than just wait to be found (Ruth 3:1-18). She can invite, she can attract, and she can gauge for herself his willingness to pursue. It’s not wrong to invite a guy to spend time with you and then see how he responds.
By doing something you will find answers a lot faster than just waiting. When you act you can gauge the man’s response and quickly understand if he is interested or not. By talking to him more, building a friendship, and just being inviting towards him, you are not pursuing a man but you are giving him opportunities to pursue you.
In short, by being a little more proactive you can save yourself a lot of time, stress, and confusion. Christian woman should not feel they are held captive to the man’s timetable. She shouldn’t be pushy, but she should not be too passive either.